Sensorless Control of Permanent-Magnet Synchronous Motor Drives Perera, Chandana

Transcription

1 Aalbog Univesitet Sensoless Contol of Pemanent-Magnet Synchonous Moto Dives Peea, Chandana Publication date: 22 Document Vesion Publishe's PDF, also known as Vesion of ecod Link to publication fom Aalbog Univesity Citation fo published vesion (APA): Peea, P. D. C. (22). Sensoless Contol of Pemanent-Magnet Synchonous Moto Dives. Aalbog Univesitet: Institut fo Enegiteknik, Aalbog Univesitet. Geneal ights Copyight and moal ights fo the publications made accessible in the public potal ae etained by the authos and/o othe copyight ownes and it is a condition of accessing publications that uses ecognise and abide by the legal equiements associated with these ights.? Uses may download and pint one copy of any publication fom the public potal fo the pupose of pivate study o eseach.? You may not futhe distibute the mateial o use it fo any pofit-making activity o commecial gain? You may feely distibute the URL identifying the publication in the public potal? Take down policy If you believe that this document beaches copyight please contact us at vbn@aub.aau.dk poviding details, and we will emove access to the wok immediately and investigate you claim. Downloaded fom vbn.aau.dk on: juli 4, 218

2 Sensoless Contol of Pemanent-Magnet Synchonous Moto Dives By P. D. Chandana Peea Dissetation submitted to the Faculty of Engineeing & Science at Aalbog Univesity in patial fulfillment of the equiements fo the degee of docto of philosophy in Electical Engineeing INSTITUTE OF ENERGY TECHNOLOGY AALBORG UNIVERSITY AALBORG, DENMARK DECEMBER 22

3 Aalbog Univesity Institute of Enegy Technology Pontoppidanstæde 11 DK-922 Aalbog East Denmak. Copyight c P. D. Chandana Peea, 22 Pinted in Denmak by Aco Gafisk A/S, Skive Second pint, Febuay 23 ISBN ii

4 Peface This thesis is submitted to the Faculty of Engineeing and Science at Aalbog Univesity in patial fulfillment of the equiements fo the Ph.D. degee in Electical Engineeing. The poject has been followed by thee supevisos: Pofesso Fede Blaabjeg, Associate Pofesso John K. Pedesen, both fom Institute of Enegy Technology (IET) at Aalbog Univesity, and Extenal Pofesso Paul Thøgesen who is Manage of Contol Engineeing at Danfoss Dives A/S. I would like to thank all of them fo thei suppot and thei esponse to my wok duing the poject peiod. This poject has been a pat of Danfoss Pofesso Pogamme at Aalbog Univesity. I geatly appeciate the financial suppot given fom Danfoss Pofesso Pogamme to cay out this eseach poject. I would like to thank Pofesso Thomas Jahns and Pofesso Robet Loenz fo thei suppot and thei discussions with me duing my two month stay at Univesity of Wisconsin in Madison. Duing that peiod, I had the oppotunity to lean about caie signal injection method fo position and velocity estimation of an inteio type PM synchonous machine and some othe aspects elated to PM synchonous machine contol, which wee invaluable fo me. Duing the poject peiod, I had many valuable discussions with the colleagues at IET. I want to thank all of them. My thanks ae also due to the laboatoy staff of IET, who helped me to build the test system fo this poject. I am also thankful to Daiusz Swieczynski fo his assistance to solve some pogamming poblems in the test system duing his stay at IET. Finally, I would like to expess my deepest gatitude to my paents and siblings fo thei constant suppot and patience. Aalbog, Novembe 22 P. D. Chandana Peea iii

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6 Abstact The educed enegy consumption is highly demand in moto dives fo heating, ventilating, and ai conditioning (HVAC) applications. The efficiency advantage makes the pemanent-magnet (PM) synchonous machine an attactive altenative to the induction machine in dives fo those applications. In ode to use PM synchonous machines in HVAC applications, simple, low-cost contol methods ae also impotant fo them. The paticula equiement in contol of PM synchonous machines is the synchonization of the AC excitation fequency with otational speed. A shaft-mounted position senso is equied fo achieving this. This shaft-mounted position senso inceases the cost and educes the eliability in the dive system. This makes it undesiable fo HVAC applications. The objective of this eseach poject is to investigate sensoless contol methods fo PM synchonous machines with paticula attention to HVAC application equiements. The undestanding of the machine model is a key equiement fo machine contol. The mathematical models fo PM synchonous machines ae fist deived in this thesis. The contol popeties of PM synchonous machines ae discussed and they ae compaed. Since high dynamic pefomance is not a demand fo HVAC applications, a suitable contol appoach fo PM synchonous machines is V/f contol appoach. A substantial pat of this thesis is devoted to investigate V/f contol appoach fo PM synchonous machines. In ode to povide basics fo designing a V/f contolled dive, the stability chaacteistics of PM synchonous machines unde open-loop V/f contol, i.e. without having any feedback fo V/f contol, is analyzed in this thesis. The lineaized machine model is the key to analyze the stability chaacteistics. The stability analysis show that the PM synchonous machine becomes unstable afte exceeding a cetain applied fequency unde open-loop V/f contol. In ode to show how to stabilize the V/f contolled PM synchonous machines fo a wide fequency ange, a simplified small signal dynamics model fo PM synchonous machines is deived in this thesis. With the help of this model it is shown that by modulating the applied fequency popotional to the petubations in the powe the stable opeation of the machine can be achieved fo a wide fequency ange. In voltage souce invete diven dives the DC-link cuent petubations can also be used fo v

7 vi Abstact this pupose. The implementation of both these methods ae discussed in details. Fo the V/f contolled dive, a method to calculate the magnitude of the voltage with vecto compensation of the stato esistance voltage dop is poposed. The complete V/f contolled dive consists of this voltage calculation algoithm and a stabilizing loop, which modulates the applied fequency popotional to the petubations in the powe. Only two cuent sensos ae equied to measue the moto phase cuents and no oto position senso is equied fo complete implementation of the dive. This poposed sensoless V/f contolled dive system demonstates satisfactoy pefomance fo HVAC applications. Besides V/f contol appoach, the field-oiented contol appoach fo PM synchonous machines is also discussed in the thesis. The contol stuctue and the design of the contolles fo field-oiented contolled dive system ae descibed. A oto position estimation technique fo sensoless opeation of the field-oiented contolled dive system is studied in details. The estimato uses pedicto-coecto method whee the diffeence between the estimated cuent and the measued cuent (cuent eo) is used to coect a pedicted oto position. The analysis show that the coection of the pedicted oto position using cuent eos is possible in the estimation algoithm fo non-salient pole PM synchonous machines, howeve, thee ae difficulties fo salient pole PM synchonous machines. Fo salient pole PM synchonous machines moe investigations ae still equied fo accuate oto position estimation. Finally, the compaison shows that the poposed sensoless V/f contol appoach has some pomising featues fo HVAC applications compaed to the sensoless fieldoiented contol appoach investigated in the thesis.

8 Table of Contents Peface Abstact Nomenclatue iii v xi Pat I Peliminaies 1 1 Intoduction Pemanent-magnetelecticmachines ClassificationofPMelecticmachines Contol fundamentals fo PMSMs Basiccontolmethods Roto position senso elimination PMSMs vesus induction machines Objectivesandscopeofthepoject Limitations Outlineofthethesis Bibliogaphy Mathematical Models and Contol Popeties Intoduction Voltage equations in the stationay a,b,c efeence fame Voltageequationsinspacevectofom d,qmodel Tansfomation of machine vaiables to a geneal otatingefeencefame Voltage equations in stationay d,q efeence fame Voltage equations in oto d,q efeence fame Theelectomagnetictoque Mechanicalequationofthemachine Steady state model in oto d,q efeence fame Contolpopeties Nomalization Constant toque angle (α = π )contol vii

9 viii Contents Maximum toque pe ampee contol Unitypowefactocontol Constantstatofluxcontol Compaisonofcontolstategies Summay... 4 Bibliogaphy Pat II Sensoless Stable V/f Contol of PMSMs 43 3 Stability Chaacteistics of PMSMs Unde Open-Loop V/f Contol Intoduction LineaizedPMSMmodel PMSM equations in state vaiable fom Lineaization Lineaized PMSM model unde open-loop V/f contol Investigation of stability chaacteistics unde open-loop V/f contol The machine unde no-load The machine unde load Simulationsandexpeimentalesults Summay Bibliogaphy Stabilization of Open-Loop V/f Contolled PMSMs Intoduction Simplifiedsmallsignaldynamicsmodel Appoximationfothesimplification Block diagam fo simplified small signal dynamics model Simplified small signal dynamics model unde open-loop V/f contol Stabilization by fequency modulation-simplified small signal model analysis Fequency modulation using oto velocity petubations Fequency modulation using powe petubations Fequency modulation using DC-link cuent petubations Stability veification fo fequency modulation Fequency modulation using powe petubations-full small signal model analysis Implementation of the stabilizing loop Simulationsandexpeimentalesults Summay Bibliogaphy... 95

10 Contents ix 5 Sensoless Stable PMSM Dive with V/f Contol Appoach Intoduction Voltagemagnitudecontolmethod Constant V/f atiocontol Calculation of voltage magnitude with stato esistance voltage dopcompensation Thecompletedivescheme Invete nonlineaity compensation Statingofthedive Pefomanceofthedive Effect of the stabilizing loop Loaddistubanceejection Pefomancewithquadaticload Summay Bibliogaphy Pat III Sensoless Field-Oiented Contol of PMSMs Field-Oiented Contol and Estimation of Roto Position and Velocity Intoduction Roto pemanent-magnet flux oiented contolled dive system Roto position and velocity estimation techniques Back-EMFcalculationbasedmethods Statofluxlinkagebasedmethods Roto position estimation based on stato phase inductance calculation Roto position estimation based on hypothetical oto position Obsevebasedmethods Position and velocity estimation using high fequency signal injection Summay Bibliogaphy Field-Oiented Contolled Dive System with and without Position Senso Intoduction Thecontolstuctueofthedivesystem Cuentcontolle Speedcontolle Cuent efeence geneato Voltage tansfomation and PWM Thedivesystemwithpositionsenso Validation of cuent and speed contolle design The pefomance of the complete dive system

11 x Contents 7.4 SensolessContol Roto position and velocity estimation Analysis of position coection methods fo the position estimationalgoithm Simulation of the sensoless dive system V/f contol and sensoless field-oiented contol -A pefomance compaison Summay Bibliogaphy Pat IV Conclusions Conclusion Contibutionsinthethesis Futuewok Pat V Appendices 189 A Data fo the IPMSM 191 B Vaious Relationship Deivations Related to Chapte 3 and Chapte B.1 The deivation of the tansfe function fo Te unde open-loop V/f δ contolofpmsms B.2 The deivation of T e as a function of V s, ω and δ B.3 The deivation of the expession fo k e B.4 The elements of the matix A 2 (X) C Geneation of PWM 197 C.1 Spacevectomodulation C.1.1 Voltagelimit... 2 C.2 Invetenonlineaitycompensation C.2.1 DC-linkvoltageipple C.2.2 Dead-time C.2.3 Componentsvoltagedop Bibliogaphy D The Laboatoy Test System 25 D.1 Convete D.2 Digitalcontolsystem D.3 Loadcontolsystem Bibliogaphy... 29

12 Nomenclatue Abbeviations CSFC CTAC DSP EMF FOC HPF HV AC IPMSM LP F MTPAC PI PMSM PWM SPMSM SV M UPFC VSI Constant stato flux contol Constant toque angle contol Digital signal pocesso Electomotive foce Field-oiented contol High-pass filte Heating, ventilating and ai conditioning Inteio magnets type pemanent-magnet synchonous machine Low-pass filte Maximum toque pe ampee contol Popotional-Integal contol Pemanent-magnet synchonous machine with sinusoidal back-emf and without dampe windings in the oto Pulse width modulation Suface magnets type pemanent-magnet synchonous machine Space vecto modulation Unity powe facto contol Voltage souce invete Symbols a Complex vecto opeato e j 2π 3 B m E m Viscous fiction coefficient Magnitude of the oto pemanent-magnet flux induced voltage vecto in steady state xi

13 xii Nomenclatue E s i as,i bs,i cs i ds,i qs Ids,I qs I s i dc i abcs i qds J L d,l q L ls L md,l mq n p p e P e s s T T l T e v as,v bs,v cs vds,v qs Vds,V qs V s v dc v abcs v qds α δ θ Magnitude of the stato flux linkage induced voltage vecto in steady state Instantaneous stato a,b,c phase cuents Instantaneous stato cuents in oto fixed d,q fame Steady state stato cuents in oto fixed d,q fame Magnitude of the stato cuent vecto in steady state DC-link cuent Stato cuent vecto in stationay efeence fame Stato cuent vecto in oto fixed d,q fame Inetia of the moto shaft and the load system Roto d- and q- axis inductances Leakage inductance Roto d- and q- axis magnetizing inductances Pole numbe of the moto Opeato d dt Instantaneous powe input to the moto Steady state powe input to the moto Stato esistance pe phase Laplace opeato Sampling peiod Load toque Electomagnetic toque poduced by the moto Instantaneous stato a,b,c phase voltages Instantaneous stato voltages in oto fixed d,q fame Steady state stato voltages in oto fixed d,q fame Magnitude of the stato voltage vecto in steady state DC-link voltage Stato voltage vecto in stationay efeence fame Stato voltage vecto in oto fixed d,q fame Toque angle Load angle Electical oto position

14 Nomenclatue xiii λ as,λ bs,λ cs λ ds,λ qs λ s λ abcs λ qds λ m φ ψ ω ω e Stato a,b,c phase flux linkage Stato flux linkage in oto fixed d,q fame Magnitude of the stato flux linkage vecto Stato flux linkage vecto in stationay efeence fame Stato flux linkage vecto in oto fixed d,q fame Roto pemanent-magnet flux which linkages with stato Powe facto angle The angle between stato flux linkage vecto and the oto pemanent-magnet flux vecto Electical oto speed Electical speed of the applied voltage vecto to the machine Subscipts a, b, c Stato a,b,c phases n Nomalized quantity s Stato quantity Steady state quantity Supescipts ˆ Roto fixed efeence fame quantity Complex conjugate Refeence quantity Estimated quantity

15 xiv Nomenclatue

16 Pat I Peliminaies

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18 Chapte 1 Intoduction 1.1 Pemanent-magnet electic machines Pemanent-magnet (PM) electic machines ae doubly excited electic machines, which have two souces of excitation, namely, the amatue and the field. In conventional doubly excited electic machines (DC commutato machines and synchonous machines), both of these excitation souces ae electic windings connected to an extenal souce of electic enegy. In PM electic machines, the field is geneated by pemanent-magnets eliminating the equiement of field windings and extenal electical souce fo it. In contast to the conventional doubly excited electic machines, the coppe loss associated with field windings does not exist in PM electic machines inceasing the efficiency of the machine. Moeove, the use of pemanent-magnets to geneate the field allows to design these machines with less weight and compact size compaed to the conventional doubly excited electic machines. On the othe hand, in PM electic machines the pemanent-magnets geneate a constant field flux and it cannot be contolled as easy as in conventional doubly excited electic machines changing the field cuent Classification of PM electic machines In geneal, PM electic machines can be classified as shown in figue 1.1. Depending on the design of the machine whethe it fo DC o AC excitation, PM electic machines can be fist classified into two goups, namely, PMDC and PMAC type. The stuctue of PMDC machines is vey simila to the conventional DC commutato machines. The only diffeence is the use of pemanent-magnets in the place of field windings. The commutato and the bushes still exist in these machines and they still suffe the poblems associated with conventional DC commutato machines. The PMAC machines ae synchonous machines, which the field is geneated by pemanent-magnets located in the oto. In these machines, the commutato and the bushes do not exist making the machine stuctue vey simple and eliminating the 3

19 4 Chapte 1. Intoduction PM electic machines PMDC machines PMAC machines Tapezoidal type (BLDCM) Sinusoidal type (PMSM) Suface magnets type (SPMSM) Inteio magnets type (IPMSM) Figue 1.1: Classification of PM electic machines. poblems, such as bushwea, high oto inetia, which associate with PMDC machines. This makes the PMAC machines the most attactive machine type among the PM electic machines. The PMAC machines can be futhe classified into tapezoidal and sinusoidal types as shown in figue 1.1. The tapezoidal PMAC machines induce a tapezoidal back-emf voltage wavefom in each stato phase winding duing otation, wheeas sinusoidal PMAC machines induce a sinusoidal back-emf voltage wavefom. Fo toque poduction, the tapezoidal PMAC machines ae excited fom ectangula cuent wavefoms, wheeas sinusoidal PMAC machines equie sinusoidal cuent excitation of the stato. The tapezoidal PMAC machines, which ae also called bushless DC motos (BLDCM) wee developed fist because of the simple contol of those machines. Howeve, the pesence of toque ipples in those dives ejects thei usage in high pefomance motion contol applications. The development of sinusoidal PMAC machines came next in late 197s and 198s due to the possibility of high pefomance contol of those machines using vecto contol pinciples fist used fo induction machines [1]. The sinusoidal PMAC machines ae the most suitable PMAC machine type to compete with the induction machines in the most of the induction machine dive applications. Theefoe, they ae getting a gowing attention in ecent yeas. Since these machines ae closely elated to the conventional synchonous machines, they ae also called PM synchonous machines (PMSMs). It should be mentioned that except fo special applications, in geneal, the PMSMs ae not built with dampe windings in the oto, mainly due to the high manufactuing cost. Heeinafte the PMSMs efeed to PM synchonous machines without having dampe windings in the oto. Diffeent oto configuations exist fo PMSMs depending on how the magnets ae placed in the oto [1], [2]. The two common types, namely, suface magnets type and inteio magnets type ae shown in figue 1.2. In suface magnets type the magnets ae mounted on the suface of the oto coe, wheeas in inteio magnets type the magnets ae placed inside the oto coe. Heeinafte the PMSMs with suface magnets oto configuation ae efeed to as SPMSMs and PMSMs with inteio magnets oto configuation ae efeed to as IPMSMs.

20 1.2. Contol fundamentals fo PMSMs 5 Roto Stato N S S N N S N S S N q d N S S N S N q Stato d Roto Pemanent magnets S N S N N S N S Pemanent magnets (a) (b) Figue 1.2: Moto coss sections showing diffeent oto configuations fo PMSMs. (a) Suface magnets type (b) Inteio magnets type. The inteio magnets type oto configuation bings saliency chaacteistics to the machine which is not pesent in a machine with suface magnets type oto [3]. As shown in figue 1.2(a) and figue 1.2(b), the magnetic flux induced by the magnets defines the oto diect o d -axis adially though the centeline of the magnets. The oto quadatue o q -axis is othogonally (9 electical degees) placed with oto d -axis (Note that fo fou-pole design this is 45 mechanical degees as shown in figue 1.2(b)). Since the pemeability of pemanent-magnets is almost same as the ai, in inteio magnets type configuation the effective aigap of d -axis is inceased compaed to the q -axis. Theefoe, the d -axis eluctance is highe than the q -axis eluctance. This esults in the q -axis inductance is highe than the d -axis inductance, i.e. L q >L d, in IPMSMs. 1.2 Contol fundamentals fo PMSMs Since PMSMs ae synchonous machines, the accuate toque can be poduced in these machines only when the AC excitation fequency is pecisely synchonized with the oto fequency. Theefoe, the fundamental equiement in contol design of PMSMs is the assuance of pecise synchonization of machine s excitation with the oto fequency. The diect appoach to achieve this equiement is the continuous measuement of the absolute oto angula position and, the excitation of the machine accodingly as shown in figue 1.3. This concept is also known as self synchonization [1] and it assues that the PMSM does not go out of synchonization duing opeation.

21 6 Chapte 1. Intoduction Command Contolle Excitation PMSM Roto angula position senso Figue 1.3: The self synchonization concept fo PMSMs, which uses oto angula position feedback to synchonize the AC excitation and the oto fequency Basic contol methods V/f contol It is possible to design the IPMSMs with squiel cage windings (dampe windings) in the oto as shown in figue 1.4. These squiel cage oto windings ae simila to the induction machine squiel cage oto windings and they poduce asynchonous toque when the IPM oto does not otate in synchonous speed. The asynchonous toque poduced by oto squiel cage windings duing asynchonous opeation put back the IPM oto to the synchonous opeation ensuing the synchonous opeation of the IPMSM at all the time. This makes the possibility to use simple open-loop V/f contol algoithm fo this type of IPMSMs as shown in figue 1.4 to achieve speed contol fo applications like pumps and fans that do not equie fast dynamic esponse [1]. Fequency command f * Voltage calculation v * s f * PWM VSI IPMSM with oto squiel cage windings Stato Roto Roto squiel cage windings Magnets Figue 1.4: Open-loop V/f contol appoach, which can be used fo IPMSMs with oto squiel cage windings. Figue 1.4 shown V/f contol appoach fo IPMSMs with oto cage windings is simila to the one uses in induction machine V/f contol (scala contol) appoach.

22 1.2. Contol fundamentals fo PMSMs 7 Howeve, one advantage in this dive is, the oto speed is only dependent on the excitation fequency of the machine and it does not equie slip compensation equiement as it does in induction machine dives. While the IPMSMs with oto cage windings can be used to contol using the configuation shown in figue 1.4, a difficulty can be expected to contol the PMSMs without having oto cage windings using the same contol configuation. The nonexistence of the oto cage windings means that the machine does not guaantee the synchonization of the oto with the excitation fequency and the stable opeation. Theefoe, to use V/f contol appoach to the PMSMs without having oto cage windings equies oto fequency (oto speed) infomation in ode to achieve the synchonization between AC excitation fequency and oto fequency. In this case, the system should be designed to opeate in closed-loop manne as shown in figue 1.5. Fequency command f * Voltage calculation + + f v* s f PWM VSI PMSM Roto angula position senso Calculation of f d/dt Figue 1.5: windings. V/f contol appoach fo PMSMs without having oto cage Closed-loop speed and toque contol Bette pefomance compaed to the V/f contol appoach can be achieved incopoating toque and speed contol of the machine in the dive contolle. The dive contol stuctue with toque and speed contolle is shown in figue 1.6. The toque poduction of PMSMs is elated to the stato cuents and the toque contol incopoates with stato cuent contol equiing stato cuent feedback to the toque contolle as shown in figue 1.6. Moeove, as descibed in the beginning of this section, to achieve self synchonization, the oto angula position feedback is also essential fo the toque contolle. The stato cuent contol is done in field-oiented fame in the toque contolle. Theefoe, the PMSM contol with this type of toque contolle can also be efeed to as field-oiented contol. The speed contol can be achieved closing the speed feedback loop outside the inne

23 8 Chapte 1. Intoduction toque contol loop as shown in figue 1.6. The speed feedback can be deived fom the same oto angula position senso, which is used to obtain the oto position feedback. Phase cuent feedback Speed command * + T* Toque e v * Speed - s contolle contolle - PWM VSI PMSM Roto angula position senso Angula position feedback Angula velocity feedback d/dt Figue 1.6: Block diagam of PMSM contol scheme incopoating toque and speed contolle. In ode to achieve fast toque contol, diect toque contol (DTC) of PMSMs is also get some attention ecently. Accuate flux estimation and toque estimation ae equied fo DTC. A detailed discussion about DTC of PMSMs can be found in [4] Roto position senso elimination It is clea fom the above discussed contol appoaches fo PMSMs, i.e. the V/f contol appoach to the PMSMs without having oto cage windings (figue 1.5) and, the toque and speed contol appoach (figue 1.6), the equiement of oto angula position senso to achieve self synchonization in the contol. This shaft mounted position senso is not desiable in the contol system due to numbe of easons [5]. The position sensos ae expensive and they consideably incease the cost of the dive system. Moeove, a special mechanical aangement needs to be made fo mounting the position sensos and exta signal wies ae equied fom the senso to the contolle. Some type of position sensos ae tempeatue sensitive and thei accuacy degades when the system tempeatue exceeds the limits. These easons lead to the elimination of shaft mounted oto angula position senso, which is conventionally used fo self synchonization in the contol system. The contol of PMSMs using the same concepts discussed in eliminating the oto angula position senso is efeed to as sensoless contol of those machines. Fo the V/f contol appoach shown in figue 1.5 thee ae possibilities to use othe vaiables athe than oto speed to achieve self synchonization and stable opeation of the PMSM. The measuements fom the moto teminals o the DC-link in the invete may be used fo this pupose and this sensoless contol appoach fo PMSMs is shown in figue 1.7.

24 1.3. PMSMs vesus induction machines 9 Fequency command f * Voltage calculation v * s + + f f PWM VSI PMSM Measuements fom moto teminals o DC link Calculation of f Figue 1.7: V/f contol appoach fo PMSMs without using oto position senso. Fo the toque and speed contol appoach shown in figue 1.6, the basic method of eliminating the shaft mounted position senso is, the accuate estimation of oto angula position and velocity using measuements fom the moto teminals o the DC-link. This appoach is shown in figue 1.8. Phase cuent feedback Speed command * + Speed contolle - T* e Toque contolle v- s * PWM VSI PMSM Measuements fom moto teminals o DC link Roto position and velocity estimato Figue 1.8: Toque and speed contol scheme fo PMSMs eliminating oto angula position senso. 1.3 PMSMs vesus induction machines In contast to the induction machines, the PMSMs do not equie magnetizing component of stato cuent, since the excitation is povided by magnets in those machines. This causes a eduction in stato coppe loss in PMSMs. Moeove, the coppe loss associated with oto in induction machines does not exist in PMSMs. This coppe loss eduction in stato and oto significantly impoves the efficiency in PMSMs compaed to the induction machines. Howeve, it should be mentioned that duing flux

25 1 Chapte 1. Intoduction weakening egime opeation the PMSMs equie high stato cuent to weaken the flux [6],[7], inceasing the stato coppe loss. This educes the efficiency of PMSMs duing flux weakening egime opeation and both PMSMs and induction machines suffe with less efficiency chaacteistics in that egime opeation. This implies that fom efficiency point of view the PMSMs ae well suited ove the induction machines in the applications like pumps and fans, whee the machines ae opeated in constant toque egime. The gowing electical enegy consumption is one of the majo poblems that wold faces at pesent. Most of this electical enegy is consumed in moto dives and a lage faction of this moto dives consumed enegy goes to the induction machine dives with pumps and fans [8]. Theefoe, in pumps and fans dives, using PMSMs instead of using induction machines, it can be contibuted to educe the total electical enegy consumption significantly. Anothe attactive featue of PMSMs ove the induction machines is that the possibility of design them with less weight and volume. Recently, the IPMSMs wee designed with significant eduction of weight and volume ove the induction machines [9],[1]. Moeove, they also have high toque to inetia (T e /J) atio, which is highly attactive fo applications that demand fast dynamic esponse. Since PMSMs ae synchonous machines thei contol should always be incopoated with self synchonization concept as explained in 1.2. It is not a equiement fo induction machine contol since they ae asynchonous machines. This makes the main diffeence in contol concepts fo these two types of machines. 1.4 Objectives and scope of the poject In pumps and fans dives, when PMSMs ae used instead of induction machines the impovement of efficiency and its impact to the global enegy saving is clea fom the discussion in 1.3. This fact is the motivation fo this poject. If PMSMs ae to be used in pumps and fans dives, they will need contol methods, which ae moe suitable fo those applications. This poject deals with contol of PMSMs focusing on pumps and fans applications. The PMSMs basic contol methods and the easons to eliminate the oto angula position senso fom those methods ae discussed in and espectively. Fo the same easons as descibed in 1.2.2, it is obvious that the oto angula position senso is highly undesiable in pumps and fans applications and sensoless contol should be consideed. Both sensoless V/f contol appoach and sensoless toque and speed contol appoach (see figue 1.7 and figue 1.8) can be consideed as solutions fo this poject. The sensoless V/f contol appoach shown in figue 1.7 seems the most suitable contol appoach fo pumps and fans dives due its simplicity. Howeve, this appoach is

26 1.5. Outline of the thesis 11 not widely addessed in the liteatue so fa. Since high dynamic pefomance of the dive is not a demand fo pumps and fans applications simple oto position and velocity estimation technique may be possible fo the sensoless toque and speed contol appoach. Consideing these facts the objectives of this poject ae as follows. The sensoless V/f contol appoach shown in figue 1.7 should be given a consideable attention duing this poject. The modeling of the system and the designing of the whole contolle should be pesented in detail. The pefomance of the dive with this contol appoach should be analyzed. The sensoless toque and speed contol appoach shown in figue 1.8 should be pesented with design of vaious contolles (speed, toque, cuent) and design of a position and speed estimato. The attention should be paid to the simplicity in position and speed estimating algoithm. The pefomance of the dive with this contol appoach should be analyzed. A compaison is equied fo the two contol appoaches in tems of implementation simplicity and pefomance Limitations Only an inteio type PM synchonous machine without having cage windings in the oto is used as the test moto fo this poject. Recently, the IPMSMs wee designed with significantly impoved efficiency, less weight and less volume ove the induction machines [9],[1]. Theefoe, an IPMSM is a good candidate to conside in pumps and fans dives. The standad adjustable speed dive convete configuation, i.e. voltage souce invete with diode ectifie, shown in figue 1.9 is used in the moto contolle. Since the applications ae pumps and fans, the contol speed ange is limited to 1%-1% of ated speed, which is typical fo such applications. The flux weakening egime opeation of the machine is not consideed. Duing 1%-1% ated speed the contolle should be able to ovecome 5% of ated load toque step. 1.5 Outline of the thesis The thesis is oganized in the following manne in ode to pesent the wok, which has been done in the poject. Fo eadability, it is sepaated into 5 pats including one pat fo appendices.

27 12 Chapte 1. Intoduction Connected to the 3-phase AC souce Connected to the 3-phase PMSM Figue 1.9: The convete configuation used in the moto contolle. PART I Chapte 1. Peliminaies Intoduction This chapte. Chapte 2. Mathematical Models and Contol Popeties In this chapte, the mathematical models fo PMSMs ae deived. The key contol popeties of the PMSMs ae discussed and they ae compaed. PART II Chapte 3. Contol Sensoless Stable V/f Contol of PMSMs Stability Chaacteistics of PMSMs Unde Open-Loop V/f Unde open-loop V/f contol the PMSMs stability behaviou is studied in detail in this chapte. The lineaized PMSM model is descibed and the eigenvalues of the lineaized system matix ae used to study the stability chaacteistics. The compute simulations and expeimental esults ae povided to validate the stability chaacteistics of the PMSMs. Chapte 4. Stabilization of Open-Loop V/f Contolled PMSMs The methods fo stabilizing the open-loop V/f contolled PMSMs ae discussed in this chapte. A simplified lineaized model is used to investigate the stabilizing methods. The implementation of the stabilizing methods ae discussed and they ae expeimentally veified. Chapte 5. Sensoless Stable PMSM Dive with V/f Contol Appoach The complete V/f contolled PMSM dive system is discussed in this chapte. A voltage contol method with stato esistance voltage dop compensation is discussed. In ode

28 1.5. Outline of the thesis 13 to povide the stability in the system, Chapte 4 discussed stabilizing technique is used. The pefomance of the complete dive system is given. PART III Chapte 6. Velocity Sensoless Field-Oiented Contol of PMSMs Field-Oiented Contol and Estimation of Roto Position and In this chapte, the oto pemanent-magnet flux oiented contolled PMSM dive system is intoduced. The oto position and velocity estimating techniques fo this dive system ae eviewed and thei meits and demeits ae discussed. Chapte 7. Field-Oiented Contolled Dive System with and without Position Senso In this chapte, the contol stuctue of the field-oiented contolled PMSM dive system is discussed in detail. The design of cuent and speed contolle ae discussed. The pefomance of the dive system with angula position senso is examined. The oto position and velocity estimation technique fo the dive system is also investigated. PART IV Chapte 8. Conclusions Conclusion The main conclusions ae highlighted in this chapte with ecommendations fo futue wok. PART V Appendices A. Data fo the IPMSM Data fo the IPMSM used in this poject ae given in this Appendix. B. Vaious Relationship Deivations Related to Chapte 3 and Chapte 4 Some elationships, which ae equied in the discussion of Chapte 3 and Chapte 4, ae deived in this Appendix. C. Geneation of PWM The PWM geneation in the dive systems is biefly descibed hee. D. The Laboatoy Test System In this Appendix, the laboatoy test system used fo expeiments is descibed.

29 14 Chapte 1. Intoduction Bibliogaphy [1] Thomas M. Jahns, Vaiable Fequency Pemanent Magnet AC Machine Dives, Chapte 6 in Powe Electonics and Vaiable Fequency Dives, Technology and Applications, B. K. Bose, Ed., IEEE Pess, [2] Godon R. Slemon, Electical Machines fo Dives, Chapte 2 in Powe Electonics and Vaiable Fequency Dives, Technology and Applications, B. K. Bose, Ed., IEEE Pess, [3] Thomas M. Jahns, Geald B. Kliman and Thomas W. Neumann, Inteio Pemanent-Magnet Synchonous Motos fo Adjustable-Speed Dives, IEEE Tansactions on Industy Applications, Vol. IA-22, No.4, pp , July/August [4] Pete Vas, Vecto and Diect Toque Contol of Synchonous Machines, Chapte 3 in Sensoless Vecto and Diect Toque Contol, pp , Oxfod Univesity Pess, [5] Kaushik Rajashekaa and Atsuo Kawamua, Sensoless Contol of Pemanent Magnet AC Motos, In poceedings of IEEE Industial Electonics Society confeence, pp , [6] Thomas M. Jahns, Flux-Weakening Regime Opeation of an Inteio Pemanent- Magnet Synchonous Moto Dive, IEEE Tansactions on Industy Applications, Vol. IA-23, No.4, pp , July/August [7] Wene Leonhad, Vaiable Fequency Synchonous Moto Dives, Chapte 14 in Contol of Electical Dives, Spinge, [8] Flemming Abahamsen, Enegy Optimal Contol of Induction Moto Dives, Ph.D. Thesis, Institute of Enegy Technology, Aalbog Univesity, Denmak, 2. [9] Yaskawa Electic Copoation, Supe-Enegy Saving Vaiable Speed Dive, VARISPEED-686SS5, Poduct catalogue, Octobe [1] Toshihio Sawa and Kaneyuki Hamada, Intoduction to the Pemanent Magnet Moto Maket, In poceedings of the confeence Enegy Efficiency in Moto-Diven systems, pp , 1999.

30 Chapte 2 Mathematical Models and Contol Popeties 2.1 Intoduction Development of the coect machine model though the undestanding of physics of the machine is the key equiement fo any type of electical machine contol. Since in this poject an Inteio type Pemanent-Magnet Synchonous Moto (IPMSM) is used fo the investigations, the mathematical models ae developed fo an IPMSM. Howeve, to educe the complexity, the development of those models is unde some assumptions as used in many models developed fo a wide vaiety of electical machines. The basic contol popeties of IPMSMs ae also discussed and they ae compaed fo the IPMSM used in this poject. 2.2 Voltage equations in the stationay a,b,c efeence fame A conceptual diagam fo two-pole IPMSM is shown in figue 2.1. It has 3-phase stato windings conceptually shown as aa, bb and cc with thei cuent diection. These stato windings ae identical windings and symmetically displaced by 12.Theaxes as, bs and cs ae magnetic axes of the stato phases a, b and c espectively. The oto has buied magnets and, the oto diect-axis (d -axis) and the oto quadatueaxis (q -axis) ae also shown in figue 2.1. No dampe windings exist fo the IPMSM used fo the investigations fo this poject and theefoe, the dampe windings ae not consideed fo modeling. The following assumptions ae made fo the development of the IPMSM model. 1. The spatial stato phase winding distibution in the ai gap is sinusoidal. 2. No themal effect fo stato esistance and the pemanent-magnet flux. 3. No satuation effect fo the inductances. 15

31 16 Chapte 2. Mathematical Models and Contol Popeties bs a q Magnet Roto c b S N b c as a d Stato a phase winding distibution cs Figue 2.1: Conceptual diagam fo thee phase, two pole IPMSM. 4. No coe losses in the machine. The voltage equations fo the stato windings can be witten in the matix fom as v abcs = s i abcs + pλ abcs (2.2.1) whee, s is stato winding esistance pe phase, p epesents the opeato d dt and v abcs (Stato phase voltage matix), i abcs (Stato phase cuent matix) and λ abcs (Stato phase flux linkage matix) ae defined by v abcs = v as v bs ; i abcs = i as i bs ; λ abcs = λ as λ bs (2.2.2) v cs i cs λ cs No oto dampe windings in the machine and theefoe, no oto cicuit equations exist fo the machine. The stato windings flux linkage matix λ abcs is elated to the stato cuents and oto pemanent-magnet flux by the following matix equation. λ abcs = λ abcs(s) + λ abcs() (2.2.3) whee, L aas L abs L acs λ abcs(s) = L bas L bbs L bcs i abcs (2.2.4) L cas L cbs L ccs

32 2.2. Voltage equations in the stationay a,b,c efeence fame 17 sin(θ ) λ abcs() = λ m sin(θ 2π ) 3 (2.2.5) sin(θ + 2π) 3 In (2.2.4), L aas is the self inductance of phase a winding, L abs and L acs ae mutual inductances between a and b phases, a and c phases espectively. Fo self and mutual inductances of b and c phases the same notations ae used. In (2.2.5), λ m is the amplitude of the flux linkages established by the pemanent-magnets on the oto as viewed fom the stato phase windings. The inductances in (2.2.4) ae descibed below. Due to the oto saliency in IPMSM the ai gap is not unifom, and theefoe, the self and mutual inductances of stato windings ae a function of the oto position. The deivation of these oto position dependent inductances is available in details in [1]. The esults ae summaized hee as following. The stato winding self inductances ae L aas = L ls + L A L B cos2θ (2.2.6) L bbs = L ls + L A L B cos(2θ + 2π 3 ) (2.2.7) L ccs = L ls + L A L B cos(2θ 2π 3 ) (2.2.8) whee, L ls is the leakage inductance and it is the same in all thee phase windings since thee phase windings ae identical. L A and L B ae given by L A =( N s 2 )2 πµ lε 1 (2.2.9) L B = 1 2 (N s 2 )2 πµ lε 2 (2.2.1) whee, N s is numbe of tuns of each phase winding, is adius, which is fom cente of machine to the inside cicumfeence of the stato and l is the axial length of the ai gap of the machine. µ is pemeability of the ai. ε 1 and ε 2 ae defined as ε 1 = 1 2 ( ) (2.2.11) g min g max ε 2 = 1 2 ( 1 1 ) (2.2.12) g min g max whee, g min is minimum ai gap length and g max is maximum ai gap length. The mutual inductances between stato phases ae L abs = L bas = 1 2 L A L B cos(2θ 2π 3 ) (2.2.13) L acs = L cas = 1 2 L A L B cos(2θ + 2π 3 ) (2.2.14) L bcs = L cbs = 1 2 L A L B cos2θ (2.2.15)

33 18 Chapte 2. Mathematical Models and Contol Popeties Finally, the flux linkage matix λ abcs in (2.2.1) can be witten in the following fom λ as λ bs = L i as i bs λ cs i cs sin(θ ) + sin(θ 2π) 3 λ m (2.2.16) sin(θ + 2π ) 3 whee, L ls + L A L B cos2θ 1 2 L A L B cos(2θ 2π 3 ) 1 2 L A L B cos(2θ + 2π 3 ) L = 2 L A L B cos(2θ 2π 3 ) L ls + L A L B cos(2θ + 2π 3 ) 1 2 L A L B cos2θ 1 2 L A L B cos(2θ + 2π 3 ) 1 2 L A L B cos2θ L ls + L A L B cos(2θ 2π 3 ) (2.2.17) 2.3 Voltage equations in space vecto fom Anothe way to epesent the machine voltage equations is space vecto fom. Space vecto fom of the machine equations has many advantages such as compact notation, easy algebaic manipulation, vey simple gaphical intepetation. Specially, this notation is vey useful when analyzing the vecto contol based techniques of the machines. The space vecto epesentation of AC machine equations has been discussed in detail in numbe of text books ([2], [3] and [4]). The instantaneous value of the machine vaiable (cuent, voltage o flux linkage) can be epesented along the phase axis as a vecto and the space vecto coespondent to this vaiable is defined as f abcs = 2 3 [f as + af bs + a 2 f cs ] (2.3.1) whee, f as,f bs and f cs ae the instantaneous values of the machine vaiable in a, b and c phases espectively and a = e j 2π 3 (2.3.2) a 2 = e j 4π 3 (2.3.3) With the above definition fo space vecto, the conjugate of it (f abcs ) becomes f abcs = 2 3 [f as + a 2 f bs + af cs ] (2.3.4) The selection of constant 2 in the definition given in (2.3.1) guaantees that fo 3 balanced sinusoidal phase wavefoms the magnitude of the space vecto is equal to the amplitude of that phase wavefoms. The IPMSM voltage equations in space vecto fom can be obtained using the definition in (2.3.1). Multiplying the second ow of the stato voltage matix equation

34 2.3. Voltage equations in space vecto fom 19 (2.2.1) by a and the thid ow by a 2, adding the esult to the fist ow and multiplying the entie esult by 2 it can be obtained the space vecto fom of the voltage equations 3 as v abcs = s i abcs + pλ abcs (2.3.5) whee, v abcs = 2 3 (v as + av bs + a 2 v cs ), (2.3.6) i abcs = 2 3 (i as + ai bs + a 2 i cs ), (2.3.7) and λ abcs = 2 3 (λ as + aλ bs + a 2 λ cs ), (2.3.8) The flux linkage space vecto λ abcs can be obtained fom cuent space vecto i abcs and pemanent-magnet flux λ m as follows. The flux linkage matix which was given in (2.2.16) can be witten in the following fom. λ as L ls + L A 1 2 L A 1 2 L A i as λ bs = 1 2 L A L ls + L A 1 2 L A i bs L e j2θ a 2 e j2θ ae j2θ i as B a 2 e j2θ ae j2θ e j2θ i bs λ cs 1 2 L A 1 2 L 2 A L ls + L A i cs ae j2θ e j2θ a 2 e j2θ i cs L e j2θ ae j2θ a 2 e j2θ i as B + λ e jθ m λ e jθ m 2 2j 2j ae j2θ a 2 e j2θ e j2θ a 2 e j2θ e j2θ ae j2θ i bs i cs a 2 e jθ ae jθ ae jθ a 2 e jθ (2.3.9) Multiplying the second ow of this equation by a and the thid ow by a 2, adding the esult to the fist ow and multiplying the entie esult by 2, one obtains (afte 3 some simplification), λ abcs = 2 3 (λ as + aλ bs + a 2 λ cs ) = 2 3 (L ls L A)(i as + ai bs + a 2 i cs ) L B (i as + a 2 i bs + ai cs )e j2θ + λ m e j(θ π 2 ) (2.3.1) Using the basic definition fo the space vecto and its conjugate this expession becomes finally, λ abcs =(L ls L A)i abcs 3 2 L Bi abcse j2θ + λ m e j(θ π 2 ) (2.3.11) Equations (2.3.5) and (2.3.11) epesent the space vecto model of the IPMSM.

35 2 Chapte 2. Mathematical Models and Contol Popeties 2.4 d,q model Tansfomation of machine vaiables to a geneal otating efeence fame Even though the space vecto fom of machine equations becomes moe compact, the oto position dependent paametes still exist in that fom of expessions (see (2.3.11) fo the stato flux linkage vecto). Theefoe, the space vecto appoach discussed in the above section is still not a simple model, which can be used fo the analysis. A simplification can be made if the space vecto model efeed to a suitably selected otating efeence fame. In the following, it is discussed how the space vecto model tansfoms to a geneal otating efeence fame. bs Im q as Re cs d Figue 2.2: Stato thee phase axes (as,bs,cs) and geneal otating efeence fame (d,q). Figue 2.2 shows axes of efeence fo the thee stato phases as, bs and cs. Italso shows a otating set of d,q axes, whee the q-axis is located an angle θ fom the stato a phase axis. Vaiables along the as, bs and cs stato axes can be efeed to the q-and d-axes by the expessions f qs = 2 3 [f ascosθ + f bs cos(θ 2π 3 )+f cscos(θ + 2π 3 f ds = 2 3 [f assinθ + f bs sin(θ 2π 3 )+f cssin(θ + 2π 3 )] (2.4.1) )] (2.4.2) whee, f epesents any of the thee phase stato vaiables such as voltage, cuent o flux linkage. The coefficient 2 should be included in (2.4.1) and (2.4.2), since the space 3 vecto definition in (2.3.1) has the same coefficient. Since thee ae thee phases, to obtain the full tansfomation to the d, q fame it is necessay to define the thid new

36 2.4. d,q model 21 vaiable which is called zeo sequence component. The expession fo the zeo sequence component f s is f s = 1 3 [f as + f bs + f cs ] (2.4.3) In geneal applications, machines ae delta o wye connected without having a neutal etun path. Theefoe, f as + f bs + f cs = (2.4.4) and zeo sequence component does not exist. Multiplying (2.4.2) by j and subtacting it fom (2.4.1) one can obtain the space vecto efeed to the otating d, q efeence fame (f qds )as f qds = f qs jf ds = 2 3 [f ase jθ + f bs e j(θ 2π 3 ) + f cs e j(θ+ 2π 3 ) ] (2.4.5) This expession fo f qds can be witten as f qds = 2 3 e jθ [f as + af bs + a 2 f cs ] (2.4.6) Finally, using the definition in (2.3.1) fo space vectos, (2.4.6) can be witten as f qds = e jθ f abcs (2.4.7) The expession (2.4.7) descibes the tansfomation of a space vecto to a geneal otating efeence fame Voltage equations in stationay d,q efeence fame Refeing to figue 2.2, the stationay (ω = ) d,q efeence fame is defined when θ =. Theefoe, fom (2.4.7) the stationay efeence fame vectos can be obtained as f s qds = f abcs = f s qs jf s ds (2.4.8) whee, supescipt s denotes the stationay efeence fame quantities. Applying the definition in (2.4.8) to (2.3.5), the stationay efeence fame machine voltage equations can be obtained as v s qds = s i s qds + pλ s qds (2.4.9) whee, λ s qds =(L ls L A)i s qds 3 2 L B(i s qds) e j2θ + λ m e j(θ π 2 ) (2.4.1)

37 22 Chapte 2. Mathematical Models and Contol Popeties Substituting the following expessions fo complex vectos v s qds = v s qs jv s ds (2.4.11) i s qds = i s qs ji s ds (2.4.12) λ s qds = λ s qs jλ s ds (2.4.13) and equating the eal and imaginay pats in both sides of (2.4.9) and (2.4.1) one can obtain the scala fom of the machine equations in stationay efeence fame as and, v s qs = s i s qs + pλ s qs (2.4.14) v s ds = s i s ds + pλ s ds (2.4.15) λ s qs =(L ls L A 3 2 L Bcos(2θ ))i s qs L Bsin(2θ )i s ds + λ m sin(θ ) (2.4.16) λ s ds = 3 2 L Bsin(2θ )i s qs +(L ls L A L Bcos(2θ ))i s ds + λ m cos(θ ) (2.4.17) Voltage equations in oto d,q efeence fame Since θ = θ in oto d,q efeence fame, the voltage vecto in that efeence fame can be obtained multiplying the both sides of (2.3.5) by e jθ as, Using chain ule, (2.4.18) can be witten as v abcs e jθ = s i abcs e jθ + e jθ pλ abcs (2.4.18) v abcs e jθ = s i abcs e jθ + pλ abcs e jθ + jω λ abcs e jθ (2.4.19) and finally, the oto efeence fame voltage vecto can be obtained fom (2.4.19) as, v qds = s i qds + pλ qds + jω λ qds (2.4.2) whee, supescipt denotes the oto efeence fame quantities. The flux linkage vecto in oto efeence fame can be obtained as λ qds = λ abcs e jθ =(L ls L A)i abcs e jθ 3 2 L Bi abcse j2θ e jθ + λ m e j(θ π 2 ) e jθ =(L ls L A)i abcs e jθ 3 2 L Bi abcse jθ + λ m e j π 2 =(L ls L A)i qds 3 2 L B(i qds) + λ m e j π 2 (2.4.21) It should be noted that when tansfoming the flux linkage vecto to the oto d,q efeence fame the oto position dependent tems disappea in the expession as it